$($a$)$ Using Karnaugh$-$map, simplify the following Boolean function P$,$ together wit care conditions d$.$

$($b$)$ Implement simplified function P$.$

$($c$)$ If you only have NAND gates, how would you implement it in simplest way.

$F(A,B,C,D)=(B,9,11,12,13,15)$

$d(A,B,C,D)=(0,2,7,14)$